Packings of different mono-sized tetrahedral particles under 3D vibrations were studied by physical experiments and DEM simulations. The effects of vibration conditions and particle shape on the packing densification were comprehensively investigated and optimized. Corresponding characteristic microscopic properties such as coordination number (CN), particle contact type, radial distribution function (RDF), and particle orientations were numerically characterized and analyzed. The results show that the DEM model can be well validated by physical experiments. Microscopic analysis indicates that the minimum mean CN appears for tetrahedral particles with regular shape. The RDF shows that as the shape deviates from regular tetrahedral particles, the frequency of face-face, vertex-face and edge-edge contacts all decreases while that of edge-face contact increases. The cluster evolutions demonstrate that the reduction or disappearance of two important local clusters (dimer and wagon wheel structures) is one of the main reasons for the decrease of packing density of irregular tetrahedral particles. (C) 2019 Elsevier B.V. All rights reserved.